Axi-majoron for almost everything

The details of the minimal cosmological standard model (MCSM) proposed in Ref. [1] are discussed. The model is based on the scale-symmetry and the global Peccei-Quinn(PQ) symmetry with a key assumption that the latter is broken only in the gravity sector in a scale-invariant manner. We show that the model provides a quite simple unified framework for the unknown history of the universe from inflation to the epoch of big-bang nucleosynthesis, simultaneously addressing key puzzles of high energy theory and cosmology: (i) the origin of scales, (ii) primordial inflation, (iii) matter-antimatter asymmetry, (iv) tiny neutrino masses, (v) dark matter, and (vi) the strong CP-problem. Scale symmetry can be exact, and the Planck scale is dynamically generated. The presence of Gauss-Bonnet term may safely retain dangerous non-perturbative symmetry-breaking effects negligible, allowing large-field trans-Planckian inflation along the PQ-field. Iso-curvature perturbations of axi-majorons are suppressed. A sizable amount of PQ-number asymmetry is generated at the end of inflation, and conserved afterwards. Domain wall problem is absent due to the PQ-number asymmetry. Baryogenesis can be realized by either inflationary Affleck-Dine mechanism or spontaneous leptogenesis thanks to the PQ-number asymmetry, or by resonant leptogenesis. Dark matter can be purely cold axi-majorons from the mis-alignment contribution only with the symmetry-breaking scale of O(10¹²) GeV. Hot axi-majorons from the decay of the inflaton become a natural source for a sizable amount of dark radiation. Inflationary gravitational waves are expected to have information about some masse parameters of the left-handed and the right-handed neutrinos, thanks to the presence of an early matter-domination era driven by at least a long-lived right-handed neutrino species.